Perturbation expansion of the conductivity correction to the Casimir force

The perturbation expansion of the finite conductivity correction to the Casimir force is obtained up to the sixth order in the small parameter which represents the relative penetration depth of electromagnetic zero-point oscillations into the metal. Configurations consisting of two plates and a spherical lens placed above a plate axe considered. The perturbation results are shown to coincide with the results of numerical computations in the framework of plasma model to better than 1%. The influence of the errors in the value of effective plasma frequency onto the correction factor is estimated. The plasma model correction factor to the Casimir force is compared with the ones computed in the context of Drude model and on the base of optical tabulated data for the complex refractive index. The exactness of each model is determined.